Transfer matrix approach for the Kerr and Faraday rotation in layered nanostructures

TL;DR

This paper introduces a transfer matrix method to analyze optical Kerr and Faraday rotation in layered nanostructures, including atomically thin conductors like bilayer graphene, accounting for their unique optical properties.

Contribution

The paper develops a general transfer matrix approach for multilayer systems with atomically thin conductors, deriving explicit formulas for polarization rotation and ellipticity.

Findings

Calculated Kerr and Faraday angles for bilayer graphene in the quantum anomalous Hall state.

Demonstrated the method's effectiveness for multilayer dielectric structures with atomically thin layers.

Provided a framework for analyzing optical rotation in complex layered nanostructures.

Abstract

To study the optical rotation of the polarization of light incident on multilayer systems consisting of atomically thin conductors and dielectric multilayers we present a general method based on transfer matrices. The transfer matrix of the atomically thin conducting layer is obtained using the Maxwell equations. We derive expressions for the Kerr (Faraday) rotation angle and for the ellipticity of the reflected (transmitted) light as a function of the incident angle and polarization of the light. The method is demonstrated by calculating the Kerr (Faraday) angle for bilayer graphene in the quantum anomalous Hall state placed on the top of dielectric multilayers. The optical conductivity of the bilayer graphene is calculated in the framework of a four-band model.